Jacobian varieties of Shimura curves are very interesting objects. For one thing they provide a geometric relation between elliptic curves and modular forms of weight 2 (say we are over $\mathbb{Q}$). So I was wondering what happens when one consider other Shimura varieties, and to start I would be happy to understand the case of $\mathcal{A}_2$.

Are there references that discuss what kind of abelian variety is the albanese of the Siegel moduli space?

Thank you in advance!